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Harmonic Analysis On Free Groups

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Harmonic Analysis On Free Groups

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Author : Figa-Talamanca
language : en
Publisher: CRC Press
Release Date : 1983-08-17

Harmonic Analysis On Free Groups written by Figa-Talamanca and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-08-17 with Mathematics categories.

This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.

Harmonic Analysis On The Heisenberg Group

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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-24

Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-24 with Mathematics categories.

This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and, hence gives the greatest opportunity for generalizing the remarkable results of Euclidian harmonic analysis.

Harmonic Analysis On Free Groups

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Author : Alessandro Figa-Talamanca
language : en
Publisher: CRC Press
Release Date : 2020-11-26

Harmonic Analysis On Free Groups written by Alessandro Figa-Talamanca and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Mathematics categories.

Fourier Analysis On Finite Abelian Groups

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Author : Bao Luong
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-14

Fourier Analysis On Finite Abelian Groups written by Bao Luong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-14 with Mathematics categories.

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

An Introduction To Harmonic Analysis On Semisimple Lie Groups

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Author : V. S. Varadarajan
language : en
Publisher: Cambridge University Press
Release Date : 1999-07-22

An Introduction To Harmonic Analysis On Semisimple Lie Groups written by V. S. Varadarajan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-22 with Mathematics categories.

Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.

Harmonic Analysis Of Spherical Functions On Real Reductive Groups

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Author : Ramesh Gangolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Harmonic Analysis Of Spherical Functions On Real Reductive Groups written by Ramesh Gangolli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.

Harmonic Analysis On Finite Groups

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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-06

Harmonic Analysis On Finite Groups written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-06 with Mathematics categories.

Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space, this book develops the necessary tools for the asymptotic analysis of these processes. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and a presentation of the presentation theory of the symmetric group. This self-contained, detailed study culminates with case-by-case analyses of the cut-off phenomenon discovered by Persi Diaconis.

Principles Of Harmonic Analysis

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Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2014-06-21

Principles Of Harmonic Analysis written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-21 with Mathematics categories.

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

A First Course In Harmonic Analysis

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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

A First Course In Harmonic Analysis written by Anton Deitmar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

This book is intended as a primer in harmonic analysis at the un dergraduate level. All the central concepts of harmonic analysis are introduced without too much technical overload. For example, the book is based entirely on the Riemann integral instead of the more demanding Lebesgue integral. Furthermore, all topological questions are dealt with purely in the context of metric spaces. It is quite sur prising that this works. Indeed, it turns out that the central concepts theory can be explained using very little of this beautiful and useful technical background. The first aim of this book is to give a lean introduction to Fourier analysis, leading up to the Poisson summation formula. The sec ond aim is to make the reader aware of the fact that both principal incarnations of Fourier Theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

Harmonic Analysis On Semigroups

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Author : C. van den Berg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Harmonic Analysis On Semigroups written by C. van den Berg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk» is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.

Harmonic Analysis On Free Groups

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